Calculating Vertical Forces in a Cantilever Beam Setup

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SUMMARY

The discussion focuses on calculating vertical forces in a cantilever beam setup with an extension, specifically addressing how to determine these forces based solely on the mass of the beam. The user proposes a mass of 1 lb for calculation purposes. Key calculations involve using the center of gravity (CG) of the beam, with two distinct CGs identified: one at a length of 9 and another at a length of 1. The downward forces acting at these points are 0.9 lb and 0.1 lb, respectively, derived from the mass distribution along the beam.

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  • Understanding of static equilibrium principles
  • Knowledge of center of gravity (CG) calculations
  • Familiarity with cantilever beam mechanics
  • Basic proficiency in force and moment calculations
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Engineering students, structural analysts, and professionals involved in mechanical design or civil engineering who are looking to deepen their understanding of cantilever beam mechanics and static force calculations.

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Homework Statement



This is not a homework problem, but something i can't figure out how to calculate. Basically I have what is similar to a cantilever beam setup with an extension. what i need to figure out is what the vertical forces are at the two points(triangles on the attached paint drawing), and how I would Calculate that. There is no force added at any point, so it needs to be calculated solely off the mass of the beam. I don't know the mass so at this point i can just make one up as M=1lb, or whatever unit you would like. thank you in advance


Homework Equations





The Attempt at a Solution


 

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This is a static problem so the sum of moments calculated about a point = 0.
And the sum of forces upward = sum of forces downward.

You would use the cg as to where the force of the beam acts. Note that you have 2 centres of gravity - one on the length = 9 and one on the length = 1. If M=1 then on the length 9 , the force of 0.9 acts downward at a location halfway of its length (9) from the up pointing triangle, and the part of the beam of length 1, has its cg at the 0.5 mark acting with of force of 0.1 downward.
Does that help?
 
Last edited:
I believe i can figure it out, thanks for the help 256bits
 

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